Further Mathematics · Pearson Edexcel 9FM0 · Option D1 · Topic 4

Critical path analysis

Planning projects with activity networks: early and late times, critical paths, float, Gantt charts and scheduling.

  • 6 sub-topics
  • 4 in Year 12, 2 in Year 13
  • 89 practice questions
  • 6 animated lessons
Practice questions (89) Lessons Worksheets All Edexcel Further Mathematics topics

What the specification says

Every sub-topic Pearson Edexcel can examine in this topic, with its reference number from the official specification. The Y12 and Y13 tags show when each sub-topic is usually taught.

  1. 4.1Activity networksY12
  2. 4.2Precedence tablesY12
  3. 4.3Critical path analysisY12
  4. 4.4Float and Gantt chartsY12
  5. 4.5Resource histograms and levellingY13
  6. 4.6SchedulingY13

Try 3 questions

Easy, medium and hard questions from this topic, each with a worked solutions and the mark for every step. All 89 questions in this topic, free, no account needed.

Critical path analysis

Easy

Dummy activities · Year 12 · 1 mark

  1. Why is a dummy activity used in an activity network?
    (1)

Show worked solutionHide worked solution
  1. A dummy has zero duration and is drawn as a dotted line.BB: To show a dependence correctly, or so that every activity has a unique pair of events

Total1

  • M
  • A
  • B
How did it go?

Report a problem with this question

Critical path analysis

Medium

Activity networks · Year 12 · 6 marks

A project consists of the following activities (duration in days, and immediate predecessors): A (2); B (6); C (1); D (4, after A); E (6, after A, B); F (3, after C); G (6, after D, E); H (4, after E, F); I (1, after G, H).
  1. (a)
    Find the earliest start time and the latest finish time of each activity.
    (4)
  2. (b)
    State the minimum project duration.
    (1)
  3. (c)
    Explain why activity HH cannot start before day 12.
    (1)

Check your answer before you look at the solution

Show worked solutionHide worked solution

Part (a)4 marks

  1. Earliest start = largest earliest finish of the predecessors.Forward pass: A 0, B0B 0, C0C 0, D2D 2, E6E 6, F1F 1, G12G 12, H12H 12, I18I 18
  2. Latest finish = smallest latest start of the successors.Backward pass: A 6, B6B 6, C11C 11, D12D 12, E12E 12, F14F 14, G18G 18, H18H 18, I19I 19

Part (b)1 mark

  1. 19 days19\text{ days}

Part (c)1 mark

  1. It must wait for EE, FF to finish, the last of which finishes on day 12.

Total6

  • M
  • A
  • B
How did it go?

Report a problem with this question

Critical path analysis

Not needed for Year 12Hard

Resource histograms · Year 13 · 4 marks

A project has these activities (duration in days, and immediate predecessors): A (3); B (6); C (2); D (5, after A); E (7, after A, B); F (3, after C); G (6, after D, E); H (3, after E, F); I (2, after G, H). Each activity needs one worker. The minimum project duration is 21 days.
  1. (a)
    Find the number of workers needed during day 8 if every activity starts at its earliest start time.
    (2)
  2. (b)
    Calculate a lower bound for the number of workers needed to complete the project in the minimum time.
    (2)

Check your answers before you look at the solution

Show worked solutionHide worked solution

Part (a)2 marks

  1. Active from ES up to ES + duration.Activities in progress: DD, EE.
  2. 22

Part (b)2 marks

  1. Total activity time ÷ critical path length.3721\frac{37}{21}
  2. Round up.lower bound=2\text{lower bound} = 2

Total4

  • M
  • A
  • B
How did it go?

Report a problem with this question